Introduction to Maple for Engineers

This page is under construction. Some links do not work, but I intend at some point to add content there.

Welcome to Maple: in my opinion, the top example of a symbolic computation language in the world today, a product that continues to be developed and maintained by professionals around the world. These pages are intended to aid an engineering student to using and mastering the Maple environment and assumes that the user understands at least one other programming language, such as, but not restricted to, C, C++, Matlab or Python.

Setup

When you launch the Maple (the IDE version), you are welcomed with a page that allows you to select a New Document and a New Worksheet. The document format provides a word-processing interface that is useful for authoring reports that contain mathematical expressions that can be executed dynamically, but we will be using an interface closer to that of Matlab and Python: an interpreter that allows you to enter Maple statements, so be sure to select a New Worksheet. You can have multiple worksheets, each under its own tab, and you can always open a new worksheet using File→New→Worksheet Mode.

Next, we are looking to learn how to use the Maple programming language, so select Tools→Options and then select the Display tab and the first option is Input display:. From the drop-down menu, choose Maple Notation and not 2-D Math Notation. The Output display: option should be left as 2-D Math Notation.

In your worksheet, you should now see a prompt together with a blinking cursor:

[> |

If you are launching the command-line version of Maple (cmaple), you will, instead, see some ASCII art and a prompt:

    |\^/|     Maple 202? (...)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 202?
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
> _

In either case, you can now type some text and it will appear in the Courier New font. In the graphical user interface, the font will also be red and bold. In the graphical user interface, you can change the font size by selecting either of the magnifying glasses with a + (enlargen) or - (reduce).

Onto our topics:

The basics: expressions, algebra and calculus

integer and rational arithmetic (and assignments and comments)
%, %% and %%%
floating-point arithmetic
algebraic expressions
algebraic equations
mathematical constants: Pi, gamma, infinity, undefined, etc.
mathematical functions
function algebra
complex numbers
radical expressions
expression limits: limit(...)
expression differentiation:diff(...)
function differentiation: D(...)
expression integration: int(...)
expression Taylor series: series(...) and convert(..., 'polynom')
expression asymptotic series: series(...) at infinity
expression adding: add(...)
expression summation: sum(...)
expression multiplying: mul(...)
expression product: product(...)
expression plotting: plot(...)
function plotting: plot(...)
expression manipulation: expand(...), factor(...) and simplify(...)

Basic data structures: Expression sequences, sets and lists

expression sequences
lists and mod1(...)
sets and set operators union, intersect, minus, in and subset
unevaluated functions
manipulating operands: op, nops, select, remove, map

Solving algebraic equations and systems of algebraic equations

Solving recurrence relations

analytic solutions

Tables: the Maple hash map

tables

Comparison and logical operators, and flow-control statements

comparison operators: =, <>, <, <=, >=, >,
piecewise-defined expressions: piecewise(...)
logical operator
conditional statements
looping statements
discontinuities and plotting discontinuous expressions: discont(...), plot(..., 'discont' = true) and about(...)

Arrays and multi-dimensional arrays

Integral transforms (Laplace and Fourier)

Solving initial- and boundary-value problems

Integral transforms (Laplace and Fourier)

signal-processing functions: $u(t)$ and $\delta(t)$ and alias(...)
signal-processing integration: $\int_{0^-}^\infty f(t) dt$
partial-fraction decomposition: convert(..., 'parfrac')
the convolution
the Laplace transform: inttrans[laplace](...)
the Fourier transform: inttrans[fourier](...)

Linear algebra

Important: Maple does not allow for symbolic vectors and matrices; however, the entries of a given vector or matrix can be rational, floating-point, or algebraic expressions including unknowns.

Vector calculus

When you include the VectorCalculus package, it sets up an environment in which you can set the coordinate system and then proceed to perform various operations on scalar and vector fields in two and three dimensions. Thus, we will go through four examples, two in two and the other two in three dimensions. It is possible to use the tools in this package without including using with( VectorCalculus );, but this is much more tedious as the coordinate system must be passed to each function call. You are welcome to investigate this on your own.

In this, we will see use of functions such as VectorCalculus['Gradient'](...), VectorCalculus['Divergence'](...), VectorCalculus['Curl'](...), etc.

Curve fitting

The CurveFitting packages has a number of functions that are useful in fitting curves to data; however, the two that engineers will be first interested in are presented here:

point plotting: plots['pointplot'](...)
polynomial interpolation: CurveFitting['PolynomialInterpolation'](...)
least-squares best-fitting functions (or linear regression): CurveFitting['LeastSquares'](...)

Scientific constants

scientific constants: ScientificConstants['Constant'](...), $G$, $e$, $\mu_0$, $h$, etc.
elements: ScientificConstants['Element'](...), H, He, Li, Be, B, C, N, etc.

Scientific error analysis

scientific error analysis

Tolerances

Statistics

The field of statistics is vast, and therefore, it is awkward that there is a single statictics package in Maple that tries to contain all aspects of this field. In the topics below, we will focus only on topics that are related.

discrete distributions: Bernoulli(...), Binomial(...), Poisson(...)
continuous distributions: Uniform(...), Normal(...)
computational statistics: Mean(...), StandardDeviation(...), etc. of data sets